Non-parametric local capability indices for industrial planar manufacts: An application to the etching phase in the microelectronic industry

Process capability indices are routinely used to estimate the mean-variability performance of industrial products with respect to both targets and specification limits. However, when the target variable is defined over a planar surface of a manufact, it is relevant to assess the capability of the production process locally, that is, at any spatial location of the surface, in particular if the manufact has to be split into pieces to obtain single production items. In this article, focusing on the Cpk specification introduced by Clements [Qual Prog., 22, 95–100], we suggest an approach based on additive quantile models to estimate, in a Bayesian paradigm, the index locally. We demonstrate its use in the context of the etching phase of the integrated circuit fabrication process. Since capability of etching processes is typically assessed for batches of wafers, we also propose two algorithms based on resampling to perform local capability analysis at the lot level.